
where \(\rho _{\rm {c}} = 1/(l+h_{\rm {mix}}v_{\rm {f}})\)  and \(v_{\rm {f}}\)  is free-flow speed. Since we know \(V_{\rm {mix}}(\rho ,h_{\rm {acc}})=Q_{h_{\rm {mix}}}/\rho \) , \(0<V_{\rm {mix}}({\rho },{h}_{\rm {acc}})<v_{\rm {f}}\)  for all \(\alpha \in [0,1]\)  and \(\rho _{\rm {min}}< \rho < (1/l)\)  is guaranteed by \(\max \lbrace h_{\rm {acc}},h_{\rm {m}}\rbrace \le h_{\rm {max}}\)  and \(\min \lbrace h_{\rm {acc}},h_{\rm {m}}\rbrace \ge h_{\rm {min}}\) . Hence, equation (REF ) defines a reasonable fundamental diagram for mixed traffic in congested conditions.
Using an analysis method similar to the one employed in
[1]}, one can find that system (REF )-() is anisotropic.
